When I had a disabled bay marked outside the house I spoke to the council about parking in it without displaying my badge as I’ve had mine stolen before in the same way, smashed a side window to get in, they said they had my registration on record and I didn’t have to bother displaying the badge.
Initially the lady I first spoke to insisted I had to display it and if not I would get a parking ticket.
I rang a fried who is a traffic warden in my area (yes some of them are human) and he said they could not enforce on private disabled bays and they never even look at them.
I’ve been parking in the bay for 5 years without a problem and one time I actually forgot and left it on the dash I got a knock at the door from another warden who advised me not to leave it on display as they see windows smashed every other day in town to get the badges.